Cosmological probes of gravity: the gravitational wave perspective

Our understanding of the universe stands on the validity of Einstein gravity at the largest scales. Despite its tremendous success in laboratory experiments and Solar System tests, we still lack of a precise knowledge of gravity at the cosmological regime. In this talk I will present how we can achieve this using gravitational waves (GW) from merging compact objects. In particular I will describe the main signatures of beyond Einstein theories and how they can be tested on individual GW events or performing population analyses. In order to claim any modification of gravity it is essential to account for the possible degeneracies with other astrophysical processes. I will conclude with the prospects of future next generation ground-based detectors and space antennas.